Total Internal Reflection of Orbital Angular Momentum Beams

We investigate how beams with orbital angular momentum (OAM) behave under total internal reflection. This is studied in two complementary experiments: In the first experiment, we study geometric shifts of OAM beams upon total internal reflection (Goos-H\"anchen and Imbert-Fedorov shifts, for each the spatial and angular variant), and in the second experiment we determine changes in the OAM mode spectrum of a beam, again upon total internal reflection. As a result we find that in the first case, the shifts are independent of OAM and beam focussing, while in the second case, modifications in the OAM spectrum occur which depend on the input OAM mode as well as on the beam focussing. This is investigated by experiment and theory. We also show how the two methods, beam shifts on the one hand, and OAM spectrum changes on the other, are related theoretically.